A radial function can be expressed by its generator through The positive definite of the function plays an important rote in the radial basis interpolation. We can naturally use Bochner's Theorem to check if is po...A radial function can be expressed by its generator through The positive definite of the function plays an important rote in the radial basis interpolation. We can naturally use Bochner's Theorem to check if is positive definite. This requires however a n-dhnensiotial Fourier transformation and it is not very easy to calculate. Furthermore in a lot of cases we will use for spaces of various dimensions too, then for every fixed n we need do the Fourier transformation once to check if the function is positive definite in the n-di-mensional space. The completely monotone function:, which is discussed in [4] is positive definite for arbitrary space dimensions. With this technique tve can very easily characterize the positive definite, of a radial function through its generator. Unfortunately there is only a very small subset of radial function which is completely monotone. Thus this criterion excluded a lot of interesting functions such as compactly supported radial function, whcih are very useful in application. Can we find some conditions (as the completely monotone function) only for the \-dimen simial Fourier transform of the generator epto characterize a radial function 9, which is positivedefinite in n-dimensional (fixed n) spacel In this paper we defined a kind of incompletelymonotone function of order a, for a= 0,,1/2 ,1,3/2,(we denote the function class by ICM) ,in this sence a normal positvie function is in ICM a positive monotone decreasing function is inICM and a positive monotone decreasing and convex function is in ICM2- Based on this definition we get a generalized Bochner's Theorem for radial function-. If dimensional Fouriertransform of the generator of a radial function can be written as , then corre-spending radial function (x) is positive definite as a n-variate function iff F is an incomplete-ly monotone function of order a= (n- 1 )/2 (or simply In this way we have characterized the positive definite of the radial function as a n-vari-ate function through its generator in the sense of the Bocher's Theorem.展开更多
The concept of FC-closed subset in FC-space without any linear structure was introduced. Then, the generalized KKM theorem is proved for FC-closed value mappings under some conditions. The FC-space in the theorem is t...The concept of FC-closed subset in FC-space without any linear structure was introduced. Then, the generalized KKM theorem is proved for FC-closed value mappings under some conditions. The FC-space in the theorem is the generalization of L-convex space and the condition of the mapping with finitely FC-closed value is weaker than that with finitely L-closed value.展开更多
A Banach space operator satisfies generalized RakoSevi5＇s property （gw） if the complement of its upper semi B-Weyl spectrum in its approximate point spectrum is the set of eigenvalues of T which are isolated in the...A Banach space operator satisfies generalized RakoSevi5＇s property （gw） if the complement of its upper semi B-Weyl spectrum in its approximate point spectrum is the set of eigenvalues of T which are isolated in the spectrum of T. In this note, we characterize hypecyclic and supercyclic operators satisfying the property （gw）.展开更多
We propose a biased random number generation protocol whose randomness is based on the violation of the Clauser Home inequality. Non-maximally entangled state is used to maximize the Bell violation. Due to the rotatio...We propose a biased random number generation protocol whose randomness is based on the violation of the Clauser Home inequality. Non-maximally entangled state is used to maximize the Bell violation. Due to the rotational asymmetry of the quantum state, the ratio of Os to ls varies with the measurement bases. The experimental partners can then use their measurement outcomes to generate the biased random bit string. The bias of their bit string can be adjusted by altering their choices of measurement bases. When this protocol is implemented in a device-independent way, we show that the bias of the bit string can still be ensured under the collective attack.展开更多
The aim of this paper is to establish an extension of qualitative and quantitative uncertainty principles for the Fourier transform connected with the spherical mean operator.
In this paper, we introduce a generalized system (for short, GS) in real Banach spaces. Using Brouwer’s fixed point theorem, we establish some existence theorems for the generalized system without monotonicity. Furth...In this paper, we introduce a generalized system (for short, GS) in real Banach spaces. Using Brouwer’s fixed point theorem, we establish some existence theorems for the generalized system without monotonicity. Further, we extend the concept of C-strong pseudomonotonicity and extend Minty’s lemma for the generalized system. And using the Minty lemma and KKM-Fan lemma, we establish an existence theorem for the generalized system with monotonicity in real reflexive Banach spaces. As the continuation of existing studies, our paper present a series of extended results based on existing corresponding results.展开更多
Present paper deals a M/M/1:(∞;GD) queueing model with interdependent controllable arrival and service rates where- in customers arrive in the system according to poisson distribution with two different arrivals rate...Present paper deals a M/M/1:(∞;GD) queueing model with interdependent controllable arrival and service rates where- in customers arrive in the system according to poisson distribution with two different arrivals rates-slower and faster as per controllable arrival policy. Keeping in view the general trend of interdependent arrival and service processes, it is presumed that random variables of arrival and service processes follow a bivariate poisson distribution and the server provides his services under general discipline of service rule in an infinitely large waiting space. In this paper, our central attention is to explore the probability generating functions using Rouche’s theorem in both cases of slower and faster arrival rates of the queueing model taken into consideration;which may be helpful for mathematicians and researchers for establishing significant performance measures of the model. Moreover, for the purpose of high-lighting the application aspect of our investigated result, very recently Maurya [1] has derived successfully the expected busy periods of the server in both cases of slower and faster arrival rates, which have also been presented by the end of this paper.展开更多
Using the newly introduced general ordering theorem by Sh/ihandeh and Bazrafkan, we derive and generalize some quantum optical identities and give their applications.
This paper proves a power balance theorem of frequency domain. It becomes another circuit law concerning power conservation after Tellegen’s theorem. Moreover the universality and importance worth of application of t...This paper proves a power balance theorem of frequency domain. It becomes another circuit law concerning power conservation after Tellegen’s theorem. Moreover the universality and importance worth of application of the theorem are introduced in this paper. Various calculation of frequency domain in nonlinear circuit possess fixed intrinsic rule. There exists the mutual influence of nonlinear coupling among various harmonics. But every harmonic component must observe individually KCL, KVL and conservation of complex power in nonlinear circuit. It is a lossless network that the nonlinear conservative system with excited source has not dissipative element. The theorem proved by this paper can directly be used to find the main harmonic solutions of the lossless circuit. The results of solution are consistent with the balancing condition of reactive power, and accord with the traditional harmonic analysis method. This paper demonstrates that the lossless network can universally produce chaos. The phase portrait is related closely to the initial conditions, thus it is not an attractor. Furthermore it also reveals the difference between the attractiveness and boundedness for chaos.展开更多
In this paper, the one-dimensional time-homogenuous lto’s stochastic differential equations, which have degenerate and discontinuous diffusion coefficients, are considered. The non-confluent property of solutions is ...In this paper, the one-dimensional time-homogenuous lto’s stochastic differential equations, which have degenerate and discontinuous diffusion coefficients, are considered. The non-confluent property of solutions is showed under some local integrability condition on the diffusion and drift coefficients. The strong comparison theorem for solutions is also established.展开更多
This paper investigates the approach of presenting groups by generators and relations from an original angle. It starts by interpreting this familiar concept with the novel notion of “formal words” created by juxtap...This paper investigates the approach of presenting groups by generators and relations from an original angle. It starts by interpreting this familiar concept with the novel notion of “formal words” created by juxtaposing letters in a set. Taking that as basis, several fundamental results related to free groups, such as Dyck’s Theorem, are proven. Then, the paper highlights three creative applications of the concept in classifying finite groups of a fixed order, representing all dihedral groups geometrically, and analyzing knots topologically. All three applications are of considerable significance in their respective topic areas and serve to illustrate the advantages and certain limitations of the approach flexibly and comprehensively.展开更多
给出函数单向S-粗集(function one direction singular rough sets)、函数单向S-粗集对偶(dual of function one direction singular rough sets)、函数双向S-粗集(function two direction singular rough sets)与函数粗集(function rou...给出函数单向S-粗集(function one direction singular rough sets)、函数单向S-粗集对偶(dual of function one direction singular rough sets)、函数双向S-粗集(function two direction singular rough sets)与函数粗集(function roughsets)。它们都是把函数概念引入到S-粗集中,改进S-粗集得到的。函数粗集是把函数概念引入到Z.Pawlak粗集中,改进Z.Pawlak粗集得到的。函数单向S-粗集、函数单向S-粗集对偶、函数双向S-粗集是函数S-粗集的三类形式。给出函数S-粗集与S-粗集的关系;给出函数粗集与Z.Pawlak粗集的关系;给出函数S-粗集与函数粗集的关系。利用这些结果,给出函数的区间离散与有限元素集的生成、函数离散-元素集合生成原理;给出函数S-粗集生成的信息规律、函数等价类动态特性-属性补充与删除原理;给出数据拆分-合成原理、信息规律动态拆分-合成的属性特征;给出信息规律动态拆分-合成不变性原理;利用这些概念与结果,给出信息规律拆分-合成与信息图像嵌入-分离的应用,给出嵌入信息图像的分离-辨识。函数S-粗集、函数粗集是粗集理论与应用研究中的一个新的研究方向。展开更多
基金The Project is Supported by National Nature Science Foundation of China
文摘A radial function can be expressed by its generator through The positive definite of the function plays an important rote in the radial basis interpolation. We can naturally use Bochner's Theorem to check if is positive definite. This requires however a n-dhnensiotial Fourier transformation and it is not very easy to calculate. Furthermore in a lot of cases we will use for spaces of various dimensions too, then for every fixed n we need do the Fourier transformation once to check if the function is positive definite in the n-di-mensional space. The completely monotone function:, which is discussed in [4] is positive definite for arbitrary space dimensions. With this technique tve can very easily characterize the positive definite, of a radial function through its generator. Unfortunately there is only a very small subset of radial function which is completely monotone. Thus this criterion excluded a lot of interesting functions such as compactly supported radial function, whcih are very useful in application. Can we find some conditions (as the completely monotone function) only for the \-dimen simial Fourier transform of the generator epto characterize a radial function 9, which is positivedefinite in n-dimensional (fixed n) spacel In this paper we defined a kind of incompletelymonotone function of order a, for a= 0,,1/2 ,1,3/2,(we denote the function class by ICM) ,in this sence a normal positvie function is in ICM a positive monotone decreasing function is inICM and a positive monotone decreasing and convex function is in ICM2- Based on this definition we get a generalized Bochner's Theorem for radial function-. If dimensional Fouriertransform of the generator of a radial function can be written as , then corre-spending radial function (x) is positive definite as a n-variate function iff F is an incomplete-ly monotone function of order a= (n- 1 )/2 (or simply In this way we have characterized the positive definite of the radial function as a n-vari-ate function through its generator in the sense of the Bocher's Theorem.
文摘The concept of FC-closed subset in FC-space without any linear structure was introduced. Then, the generalized KKM theorem is proved for FC-closed value mappings under some conditions. The FC-space in the theorem is the generalization of L-convex space and the condition of the mapping with finitely FC-closed value is weaker than that with finitely L-closed value.
文摘A Banach space operator satisfies generalized RakoSevi5＇s property （gw） if the complement of its upper semi B-Weyl spectrum in its approximate point spectrum is the set of eigenvalues of T which are isolated in the spectrum of T. In this note, we characterize hypecyclic and supercyclic operators satisfying the property （gw）.
基金Supported by the National Natural Science Foundation of China under Grant Nos 61378011,U1204616 and 11447143the Program for Science and Technology Innovation Talents in Universities of Henan Province under Grant No 2012HASTIT028the Program for Science and Technology Innovation Research Team in University of Henan Province under Grant No 13IRTSTHN020
文摘We propose a biased random number generation protocol whose randomness is based on the violation of the Clauser Home inequality. Non-maximally entangled state is used to maximize the Bell violation. Due to the rotational asymmetry of the quantum state, the ratio of Os to ls varies with the measurement bases. The experimental partners can then use their measurement outcomes to generate the biased random bit string. The bias of their bit string can be adjusted by altering their choices of measurement bases. When this protocol is implemented in a device-independent way, we show that the bias of the bit string can still be ensured under the collective attack.
文摘The aim of this paper is to establish an extension of qualitative and quantitative uncertainty principles for the Fourier transform connected with the spherical mean operator.
文摘In this paper, we introduce a generalized system (for short, GS) in real Banach spaces. Using Brouwer’s fixed point theorem, we establish some existence theorems for the generalized system without monotonicity. Further, we extend the concept of C-strong pseudomonotonicity and extend Minty’s lemma for the generalized system. And using the Minty lemma and KKM-Fan lemma, we establish an existence theorem for the generalized system with monotonicity in real reflexive Banach spaces. As the continuation of existing studies, our paper present a series of extended results based on existing corresponding results.
文摘Present paper deals a M/M/1:(∞;GD) queueing model with interdependent controllable arrival and service rates where- in customers arrive in the system according to poisson distribution with two different arrivals rates-slower and faster as per controllable arrival policy. Keeping in view the general trend of interdependent arrival and service processes, it is presumed that random variables of arrival and service processes follow a bivariate poisson distribution and the server provides his services under general discipline of service rule in an infinitely large waiting space. In this paper, our central attention is to explore the probability generating functions using Rouche’s theorem in both cases of slower and faster arrival rates of the queueing model taken into consideration;which may be helpful for mathematicians and researchers for establishing significant performance measures of the model. Moreover, for the purpose of high-lighting the application aspect of our investigated result, very recently Maurya [1] has derived successfully the expected busy periods of the server in both cases of slower and faster arrival rates, which have also been presented by the end of this paper.
基金Project supported by the Imam Khomeini International University,I. R. Iran (Grant Nos. 751075-91 and 383042-91)
文摘Using the newly introduced general ordering theorem by Sh/ihandeh and Bazrafkan, we derive and generalize some quantum optical identities and give their applications.
文摘This paper proves a power balance theorem of frequency domain. It becomes another circuit law concerning power conservation after Tellegen’s theorem. Moreover the universality and importance worth of application of the theorem are introduced in this paper. Various calculation of frequency domain in nonlinear circuit possess fixed intrinsic rule. There exists the mutual influence of nonlinear coupling among various harmonics. But every harmonic component must observe individually KCL, KVL and conservation of complex power in nonlinear circuit. It is a lossless network that the nonlinear conservative system with excited source has not dissipative element. The theorem proved by this paper can directly be used to find the main harmonic solutions of the lossless circuit. The results of solution are consistent with the balancing condition of reactive power, and accord with the traditional harmonic analysis method. This paper demonstrates that the lossless network can universally produce chaos. The phase portrait is related closely to the initial conditions, thus it is not an attractor. Furthermore it also reveals the difference between the attractiveness and boundedness for chaos.
文摘In this paper, the one-dimensional time-homogenuous lto’s stochastic differential equations, which have degenerate and discontinuous diffusion coefficients, are considered. The non-confluent property of solutions is showed under some local integrability condition on the diffusion and drift coefficients. The strong comparison theorem for solutions is also established.
文摘This paper investigates the approach of presenting groups by generators and relations from an original angle. It starts by interpreting this familiar concept with the novel notion of “formal words” created by juxtaposing letters in a set. Taking that as basis, several fundamental results related to free groups, such as Dyck’s Theorem, are proven. Then, the paper highlights three creative applications of the concept in classifying finite groups of a fixed order, representing all dihedral groups geometrically, and analyzing knots topologically. All three applications are of considerable significance in their respective topic areas and serve to illustrate the advantages and certain limitations of the approach flexibly and comprehensively.
文摘给出函数单向S-粗集(function one direction singular rough sets)、函数单向S-粗集对偶(dual of function one direction singular rough sets)、函数双向S-粗集(function two direction singular rough sets)与函数粗集(function roughsets)。它们都是把函数概念引入到S-粗集中,改进S-粗集得到的。函数粗集是把函数概念引入到Z.Pawlak粗集中,改进Z.Pawlak粗集得到的。函数单向S-粗集、函数单向S-粗集对偶、函数双向S-粗集是函数S-粗集的三类形式。给出函数S-粗集与S-粗集的关系;给出函数粗集与Z.Pawlak粗集的关系;给出函数S-粗集与函数粗集的关系。利用这些结果,给出函数的区间离散与有限元素集的生成、函数离散-元素集合生成原理;给出函数S-粗集生成的信息规律、函数等价类动态特性-属性补充与删除原理;给出数据拆分-合成原理、信息规律动态拆分-合成的属性特征;给出信息规律动态拆分-合成不变性原理;利用这些概念与结果,给出信息规律拆分-合成与信息图像嵌入-分离的应用,给出嵌入信息图像的分离-辨识。函数S-粗集、函数粗集是粗集理论与应用研究中的一个新的研究方向。
